A $q$-anaolg of the sixth Painlevé equation

Details A $q$-anaolg of the sixth Painlevé equation A $q$-anaolg of the sixth Painlevé equation

1995-07-31

arxiv.org/abs/chao-dyn/9507010v2

Nonlinear Sciences

Chaotic Dynamics

8 pages, LaTeX file (Two misprints corrected)

Scientific paper

10.1007/BF00398316

A $q$-difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
$q$-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of $q$-hypergeometric functions are also discussed.

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